What Does Compound Mean?
Compound, to savers and investors, means the ability of a sum of money to grow exponentially over time by the repeated addition of earnings to the principal invested. Each round of earnings adds to the principal that yields the next round of earnings.
In savings accounts, this is called compound interest.
By contrast, simple interest does not reflect compounding. The interest is paid on the original balance only, not the original balance plus its previous earnings.
Understanding Compound Interest
Suppose you invest $10,000 into company XYZ. The first year, the shares rise 20%. Your investment is now worth $12,000. Based on its good performance, you hold onto the stock. In Year 2, the shares appreciate another 20%. Your $12,000 investment has now grown to $14,400.
Compounding is the repeated addition of interest payments to the principal invested over a period of time.
The principal grows exponentially as each new payment of interest is added to it.
Simple interest is paid only on the original amount invested, growing more slowly over time.
Rather than your shares appreciating an additional $2,000 (20%)m as they did in the first year, they appreciate an additional $400, because the $2,000 you gained in the first year grew by 20% as well.
If you extrapolate the process out, the numbers start to get very big as your previous earnings start to provide further returns. In fact, $10,000 invested at 20% annually for 25 years would grow to nearly $1,000,000, and that's without adding any money to the original amount invested.
The power of compounding was called the eighth wonder of the world by Albert Einstein, or so the story goes. He also is said to have declared that "He who understands it, earns it. He who doesn't, pays it."
The Formula for Compounding
The formula for calculating compound interest is as follows:
= [P (1 + i)n] – P
= P [(1 + i)n – 1]
(Where P = Principal, i = nominal annual interest rate in percentage terms, and n = number of compounding periods.)
Don't forget to adjust the "i" and "n" If the number of compounding periods is more than once a year.
Example of Compound Interest Calculation
Take a three-year loan of $10,000 at an interest rate of 5% that compounds annually. What would be the amount of interest? In this case, it would be: $10,000 [(1 + 0.05)3] – 1 = $10,000 [1.157625 – 1] = $1,576.25.
When calculating compound interest, the number of compounding periods makes a significant difference. The higher the number of compounding periods, the greater the amount of compound interest will be.
If the number of compounding periods is more than once a year, "i" and "n" must be adjusted accordingly. The "i" must be divided by the number of compounding periods per year, and "n" is the number of compounding periods per year times the loan or deposit’s maturity period in years.
Investor.gov, a website operated by the U.S. Securities and Exchange Commission, offers a free online compound interest calculator. The calculator allows the input of monthly deposits made to the principal, which is helpful for regular savers.